Fairly easy here. Его and её only take initial «н» as pronouns in Genitive case (and, well, Accusative, because it's the same). When you have possessive adjective pronouns «его» and «её», no «н» is required.
Though, of course, these possessive adjectives (его, её, их) originate from the Genitive case of the corresponding pronouns.
As a bonus, you can consider the initial «н» a sure sign that the preposition really refers to the pronoun (remember that not all preposition require it!) :
- Я от неё писем не получал. → «от» refers to some «она» ("I haven't received any letters from her")
- Я от её писем уже устал. → «от» is a preposition before «писем», and «её» is a possessive adjective that got between them ("I am tired of her letters already").